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Theory And Calibration Of Swap Market Models
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Book Synopsis Theory and Calibration of Swap Market Models by : Stefano Galluccio
Download or read book Theory and Calibration of Swap Market Models written by Stefano Galluccio and published by . This book was released on 2007 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper introduces a general framework for market models, named Market Model Approach, through the concept of admissible sets of for-ward swap rates spanning a given tenor structure. We relate this concept to results in graph theory by showing that a set is admissible if and only if the associated graph is a tree. This connection enables us to enumerate all admissible models for a given tenor structure. Three main classes are identified within this framework, and correspond to the co-terminal, co-initial, and co-sliding model. We prove that the LIBOR market model is the only admissible model of a co-sliding type. By focusing on the co-terminal model in a lognormal setting, we develop and compare several approximating analytical formulae for caplets, while swaptions can be priced by a simple Black-type formula. A novel calibration technique is introduced to allow simultaneous calibration to caplet and swaption prices. Empirical calibration of the co-terminal model is shown to be faster, more robust and more efficient than the same procedure applied to the LIBOR market model. We then argue that the co-terminal approach is the simplest and most convenient market model for pricing and hedging a large variety of exotic interest-rate derivatives.
Book Synopsis Theory and Calibration of Swap Market Models by :
Download or read book Theory and Calibration of Swap Market Models written by and published by . This book was released on 2004 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The SABR/LIBOR Market Model by : Riccardo Rebonato
Download or read book The SABR/LIBOR Market Model written by Riccardo Rebonato and published by John Wiley & Sons. This book was released on 2009-04-13 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a major innovation in the interest rate space. It explains a financially motivated extension of the LIBOR Market model which accurately reproduces the prices for plain vanilla hedging instruments (swaptions and caplets) of all strikes and maturities produced by the SABR model. The authors show how to accurately recover the whole of the SABR smile surface using their extension of the LIBOR market model. This is not just a new model, this is a new way of option pricing that takes into account the need to calibrate as accurately as possible to the plain vanilla reference hedging instruments and the need to obtain prices and hedges in reasonable time whilst reproducing a realistic future evolution of the smile surface. It removes the hard choice between accuracy and time because the framework that the authors provide reproduces today's market prices of plain vanilla options almost exactly and simultaneously gives a reasonable future evolution for the smile surface. The authors take the SABR model as the starting point for their extension of the LMM because it is a good model for European options. The problem, however with SABR is that it treats each European option in isolation and the processes for the various underlyings (forward and swap rates) do not talk to each other so it isn't obvious how to relate these processes into the dynamics of the whole yield curve. With this new model, the authors bring the dynamics of the various forward rates and stochastic volatilities under a single umbrella. To ensure the absence of arbitrage they derive drift adjustments to be applied to both the forward rates and their volatilities. When this is completed, complex derivatives that depend on the joint realisation of all relevant forward rates can now be priced. Contents THE THEORETICAL SET-UP The Libor Market model The SABR Model The LMM-SABR Model IMPLEMENTATION AND CALIBRATION Calibrating the LMM-SABR model to Market Caplet prices Calibrating the LMM/SABR model to Market Swaption Prices Calibrating the Correlation Structure EMPIRICAL EVIDENCE The Empirical problem Estimating the volatility of the forward rates Estimating the correlation structure Estimating the volatility of the volatility HEDGING Hedging the Volatility Structure Hedging the Correlation Structure Hedging in conditions of market stress
Book Synopsis The LIBOR Market Model in Practice by : Dariusz Gatarek
Download or read book The LIBOR Market Model in Practice written by Dariusz Gatarek and published by John Wiley & Sons. This book was released on 2007-01-30 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: The LIBOR Market Model (LMM) is the first model of interest rates dynamics consistent with the market practice of pricing interest rate derivatives and therefore it is widely used by financial institution for valuation of interest rate derivatives. This book provides a full practitioner's approach to the LIBOR Market Model. It adopts the specific language of a quantitative analyst to the largest possible level and is one of first books on the subject written entirely by quants. The book is divided into three parts - theory, calibration and simulation. New and important issues are covered, such as various drift approximations, various parametric and nonparametric calibrations, and the uncertain volatility approach to smile modelling; a version of the HJM model based on market observables and the duality between BGM and HJM models. Co-authored by Dariusz Gatarek, the 'G' in the BGM model who is internationally known for his work on LIBOR market models, this book offers an essential perspective on the global benchmark for short-term interest rates.
Book Synopsis Interest Rate Models - Theory and Practice by : Damiano Brigo
Download or read book Interest Rate Models - Theory and Practice written by Damiano Brigo and published by Springer Science & Business Media. This book was released on 2007-09-26 with total page 1016 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 2nd edition of this successful book has several new features. The calibration discussion of the basic LIBOR market model has been enriched considerably, with an analysis of the impact of the swaptions interpolation technique and of the exogenous instantaneous correlation on the calibration outputs. A discussion of historical estimation of the instantaneous correlation matrix and of rank reduction has been added, and a LIBOR-model consistent swaption-volatility interpolation technique has been introduced. The old sections devoted to the smile issue in the LIBOR market model have been enlarged into a new chapter. New sections on local-volatility dynamics, and on stochastic volatility models have been added, with a thorough treatment of the recently developed uncertain-volatility approach. Examples of calibrations to real market data are now considered. The fast-growing interest for hybrid products has led to a new chapter. A special focus here is devoted to the pricing of inflation-linked derivatives. The three final new chapters of this second edition are devoted to credit. Since Credit Derivatives are increasingly fundamental, and since in the reduced-form modeling framework much of the technique involved is analogous to interest-rate modeling, Credit Derivatives -- mostly Credit Default Swaps (CDS), CDS Options and Constant Maturity CDS - are discussed, building on the basic short rate-models and market models introduced earlier for the default-free market. Counterparty risk in interest rate payoff valuation is also considered, motivated by the recent Basel II framework developments.
Book Synopsis The Swap Market Model with Local Stochastic Volatility by : Kenjiro Oya
Download or read book The Swap Market Model with Local Stochastic Volatility written by Kenjiro Oya and published by . This book was released on 2018 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this paper is to present the multi-factor swap market model with non-parametric local volatility functions and stochastic volatility scaling factors. We provide a Dupire-like formula with which calibration can be carried out with the particle algorithm in an efficient manner. We also discuss how the calibration method can be made applicable in the context of Libor Market Model. We show high accuracy of our calibration algorithm by numerical experiments.
Book Synopsis Interest Rate Models Theory and Practice by : Damiano Brigo
Download or read book Interest Rate Models Theory and Practice written by Damiano Brigo and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 2nd edition of this successful book has several new features. The calibration discussion of the basic LIBOR market model has been enriched considerably, with an analysis of the impact of the swaptions interpolation technique and of the exogenous instantaneous correlation on the calibration outputs. A discussion of historical estimation of the instantaneous correlation matrix and of rank reduction has been added, and a LIBOR-model consistent swaption-volatility interpolation technique has been introduced. The old sections devoted to the smile issue in the LIBOR market model have been enlarged into a new chapter. New sections on local-volatility dynamics, and on stochastic volatility models have been added, with a thorough treatment of the recently developed uncertain-volatility approach. Examples of calibrations to real market data are now considered. The fast-growing interest for hybrid products has led to a new chapter. A special focus here is devoted to the pricing of inflation-linked derivatives. The three final new chapters of this second edition are devoted to credit. Since Credit Derivatives are increasingly fundamental, and since in the reduced-form modeling framework much of the technique involved is analogous to interest-rate modeling, Credit Derivatives -- mostly Credit Default Swaps (CDS), CDS Options and Constant Maturity CDS - are discussed, building on the basic short rate-models and market models introduced earlier for the default-free market. Counterparty risk in interest rate payoff valuation is also considered, motivated by the recent Basel II framework developments.
Book Synopsis Libor Market Mode - Theory and Practice by : Irina Götsch
Download or read book Libor Market Mode - Theory and Practice written by Irina Götsch and published by GRIN Verlag. This book was released on 2006-03-26 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: Diploma Thesis from the year 2006 in the subject Economics - Monetary theory and policy, grade: 2.0, University of Frankfurt (Main), language: English, abstract: The goal of this thesis is to examine the LMM theoretically and apply practically to derivatives pricing. The input data structuring and calibration to market and historical data, implementing and pricing issues will be specifically investigated. This work begins with the comparison of the LMM to alternative interest rate models in chapter 2. A review of basic theory of the valuation of derivatives, which will be used in the next chapters, is presented in chapter 3. Theoretical description of the LMM is presented in the next chapter. Chapter 5 investigates several methods of calibrating directly to market cap and swaption prices. The way of obtaining the initial Libor yield curve is also summarized. In chapter 6 and 7 modeling of forward Libor rates volatility and correlation is presented. Hedging issues are to find in chapter 8. Chapter 9 covers pricing with the LMM by Monte Carlo simulations. This chapter presents the results of imple-menting the cascade calibration and of valuation of derivatives to illustrate the performance of the LMM. Finally the last chapter summarises and concludes the thesis.
Book Synopsis Interest Rate Swaps and Their Derivatives by : Amir Sadr
Download or read book Interest Rate Swaps and Their Derivatives written by Amir Sadr and published by John Wiley & Sons. This book was released on 2009-08-07 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: An up-to-date look at the evolution of interest rate swaps and derivatives Interest Rate Swaps and Derivatives bridges the gap between the theory of these instruments and their actual use in day-to-day life. This comprehensive guide covers the main "rates" products, including swaps, options (cap/floors, swaptions), CMS products, and Bermudan callables. It also covers the main valuation techniques for the exotics/structured-notes area, which remains one of the most challenging parts of the market. Provides a balance of relevant theory and real-world trading instruments for rate swaps and swap derivatives Uses simple settings and illustrations to reveal key results Written by an experienced trader who has worked with swaps, options, and exotics With this book, author Amir Sadr shares his valuable insights with practitioners in the field of interest rate derivatives-from traders and marketers to those in operations.
Download or read book Swap market model written by Bing Gan and published by . This book was released on 2008 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Modeling And Pricing Of Swaps For Financial And Energy Markets With Stochastic Volatilities by : Anatoliy Swishchuk
Download or read book Modeling And Pricing Of Swaps For Financial And Energy Markets With Stochastic Volatilities written by Anatoliy Swishchuk and published by World Scientific. This book was released on 2013-06-03 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modeling and Pricing of Swaps for Financial and Energy Markets with Stochastic Volatilities is devoted to the modeling and pricing of various kinds of swaps, such as those for variance, volatility, covariance, correlation, for financial and energy markets with different stochastic volatilities, which include CIR process, regime-switching, delayed, mean-reverting, multi-factor, fractional, Levy-based, semi-Markov and COGARCH(1,1). One of the main methods used in this book is change of time method. The book outlines how the change of time method works for different kinds of models and problems arising in financial and energy markets and the associated problems in modeling and pricing of a variety of swaps. The book also contains a study of a new model, the delayed Heston model, which improves the volatility surface fitting as compared with the classical Heston model. The author calculates variance and volatility swaps for this model and provides hedging techniques. The book considers content on the pricing of variance and volatility swaps and option pricing formula for mean-reverting models in energy markets. Some topics such as forward and futures in energy markets priced by multi-factor Levy models and generalization of Black-76 formula with Markov-modulated volatility are part of the book as well, and it includes many numerical examples such as S&P60 Canada Index, S&P500 Index and AECO Natural Gas Index.
Book Synopsis Understanding Swaps by : John Francis Marshall
Download or read book Understanding Swaps written by John Francis Marshall and published by University of Texas Press. This book was released on 1993-11-08 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by international experts on the theory and practice of swaps, this primer provides a conceptual and practical framework for grasping the seemingly complex field of swaps. Includes examples that show how complex financial structures can be built by using a number of different swaps.
Book Synopsis Calibration and Parameterization Methods for the Libor Market Model by : Christoph Hackl
Download or read book Calibration and Parameterization Methods for the Libor Market Model written by Christoph Hackl and published by Springer Science & Business Media. This book was released on 2013-12-27 with total page 69 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Libor Market Model (LMM) is a mathematical model for pricing and risk management of interest rate derivatives and has been built on the framework of modelling forward rates. For the conceptual understanding of the model a strong background in the fields of mathematics, statistics, finance and especially for implementation, computer science is necessary. The book provides the ne cessary groundwork to understand the LMM and delivers a framework to implement a working model where possible calibration and parameterization methods for volatility and correlation are explained. Special emphasis lies also on the trade off of speed and correctness where differences in choosing random number generators and the advantages of factor reduction are shown.
Book Synopsis The Co-Initial Swap Market Model by : Stefano Galluccio
Download or read book The Co-Initial Swap Market Model written by Stefano Galluccio and published by . This book was released on 2005 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we introduce a new approach to the pricing and the risk-management of generic European-style interest rate derivatives. This approach has great flexibility and has the advantage of avoiding complex model calibration techniques typical of standard short-rate models. Dynamics are assigned on a set of co-initial forward swap rates and arbitrage-free restrictions are determined in a normal and lognormal setup. Model implementation and calibration are discussed and details of two example applications are also presented.See published version of this paper located at: http://ssrn.com/abstract=595077.
Book Synopsis Modern Pricing of Interest-Rate Derivatives by : Riccardo Rebonato
Download or read book Modern Pricing of Interest-Rate Derivatives written by Riccardo Rebonato and published by Princeton University Press. This book was released on 2012-01-16 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, interest-rate modeling has developed rapidly in terms of both practice and theory. The academic and practitioners' communities, however, have not always communicated as productively as would have been desirable. As a result, their research programs have often developed with little constructive interference. In this book, Riccardo Rebonato draws on his academic and professional experience, straddling both sides of the divide to bring together and build on what theory and trading have to offer. Rebonato begins by presenting the conceptual foundations for the application of the LIBOR market model to the pricing of interest-rate derivatives. Next he treats in great detail the calibration of this model to market prices, asking how possible and advisable it is to enforce a simultaneous fitting to several market observables. He does so with an eye not only to mathematical feasibility but also to financial justification, while devoting special scrutiny to the implications of market incompleteness. Much of the book concerns an original extension of the LIBOR market model, devised to account for implied volatility smiles. This is done by introducing a stochastic-volatility, displaced-diffusion version of the model. The emphasis again is on the financial justification and on the computational feasibility of the proposed solution to the smile problem. This book is must reading for quantitative researchers in financial houses, sophisticated practitioners in the derivatives area, and students of finance.
Book Synopsis Generalized Swap Market Model and the Valuation of Interest Rate Derivatives by : Jianwei Zhu
Download or read book Generalized Swap Market Model and the Valuation of Interest Rate Derivatives written by Jianwei Zhu and published by . This book was released on 2008 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we will establish a generalized Swap Market Model (GSMM) by unifying the stochastic process of swap rates with constant tenors under a single swap measure. GSMM is a natural extension of Libor Market Model (LMM) for swap rates, and LMM can be considered as a special case of GSMM since Libors is a special swap rate with the constant tenor of one period. GSMM can be applied for pricing and hedging any interest rate derivatives, and is suited especially for CMS and swap rate products. There are a number advantages of GSMM: (1) GSMM models swap rates directly, and therefore achieves the best match between products and model. (2) GSMM can be calibrated to the term structure of swaption volatilities easily and quickly. (3) There is no translation of risk sensitivities with respect to swap rates within GSMM. In contrast, risk sensitives such as Vega for swap rates can not be derived directly, and must be translated in an inefficient, inaccurate and nontransparent manner in the most existing interest rate models. (4) All smile modelings for LMM can be taken over for GSMM since GSMM and LMM share an almost identical mathematical structure. (5) GSMM avoids the inconsistency of the market conventions in cap and swaptions markets. Accompanied by these favorite features, GSMM should be a promising interest rate model for pricing and hedging most traded swap rate structures in financial market.
Book Synopsis Stochastic Volatility Extensions of the Swap Market Model by : Milena Gueorguieva Tzigantcheva
Download or read book Stochastic Volatility Extensions of the Swap Market Model written by Milena Gueorguieva Tzigantcheva and published by . This book was released on 2008 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: ABSTRACT: Two stochastic volatility extensions of the Swap Market Model, one with jumps and the other without, are derived. In both stochastic volatility extensions of the Swap Market Model the instantaneous volatility of the forward swap rates evolves according to a square-root diffusion process. In the jump-diffusion stochastic volatility extension of the Swap Market Model, the proportional log-normal jumps are applied to the swap rate dynamics. The speed, the flexibility and the accuracy of the fast fractional Fourier transform made possible a fast calibration to European swaption market prices. A specific functional form of the instantaneous swap rate volatility structure was used to meet the observed evidence that volatility of the instantaneous swap rate decreases with longer swaption maturity and with larger swaption tenors.
